Chapter 12: Applications of Database Marketing in B-to-C and B-to-B Scenarios

Customer Relationship Management A Databased Approach V. Kumar Werner J. Reinartz Instructor’s Presentation Slides

Chapter Twelve Applications of Database Marketing in B-to-C and B-to-B Scenarios

Topics Discussed

Customer Value- A Decision Metric

Study 1: The Life-time-Profitability Relationship in a Non-contractual Setting

Study 2: A model for incorporating customers’ projected profitability into lifetime duration computation

Study 3: A model for identifying the true value of a lost customer

Study 1:The Life-time-Profitability Relationship in a Non-contractual Setting

Background and Objective

The firm has to ensure that the relationship stays alive since the customer typically splits his/her category expenses with several firms

Objectives:

Test for the strength of the lifetime duration – profitability relationship

Whether profits increase over time (lifetime profitability pattern)

Whether the costs of serving long-life customers are actually less

Whether long-life customers pay higher prices

Study 1 (contd.)

Conceptual Model

To investigate the consequences of customer retention, namely, profitability:

Individual customer lifetime profits are modeled as a function of a customer’s lifetime duration

Revenue flows over the course of a customer’s lifetime

Firm cost is associated with the marketing exchange

Customer Lifetime and Firm Profitability:

Proposition 1:The Nature of the Lifetime-Profitability Relationship is Positive

Lifetime-Profitability Association Segmentation Scheme

Lifetime Profit Low High Lifetime revenue High Low Short Long Lifetime duration Segment 2 Segment 3 Segment 4 Segment 1 Long Lifetime Duration Short

Customer Lifetime and Firm Profitability : Proposition 2: Profits Increase over Time

Analysis of the dynamic aspects of the lifetime-profitability relationship

Non-contractual setting: cost of serving customer can easily exceed the profit margin brought in by the customer. Therefore, profits may not increase over time

Example: catalog shopping or direct mail offerings - the customer may end up buying once a year and spend a smaller amount

Whether there is lower transaction costs for longer-life versus shorter-life customers (e.g.: retail sector)

Whether the costs associated with promotional expenditures directed at longer- and shorter-life customers actually differ

Proposition 3: The Costs of Serving Longer-life Customers are lower

Proposition 4: Longer-life Customers Pay Higher Prices

Existing customers pay effectively higher prices than new ones, even after accounting for possible introductory offers

OR

Higher value consciousness of long-term customers because customers learn over time to trust lower priced items or brands rather than established name brand products

Model for Measuring Customer Lifetime for Non-Contractual Relationships

Negative Binomial Distribution (NBD)/Pareto model

Based on the customer-specific probability of being alive, the model can be used to determine which customers should be deleted from active status

Given that the outcome of the NBD/Pareto model is a continuous probability estimate, continuous P(Alive) estimate is transformed into a dichotomous “alive/dead” measure

Knowing a person’s “time of birth” and given a specified probability level threshold), can approximate when a customer is deemed to have left the relationship

The time from birth, t 0 , until the date associated with the cut-off threshold, t cut-off , constitutes the lifetime of the customer

Calculate finite lifetime for each customer, for profitability analysis

Research Methodology

Illustrative Lifetime Determination of Individual Household Source: Reinartz W. And Kumar V., “On the Profitability of Long –life Customers in a Non-Contractual Setting: An empirical Investigation and Implications for Marketing

Measuring Customer Lifetime for Non-Contractual Relationships (contd.)

Establishment of Cut-off Threshold

E stablishment of cut-off threshold that produces the highest percentage of correct classifications (here 0.5)

Lifetime Estimation

Finite Lifetime Estimates

35 12 41.7 7.9 27.9 Cohort 2 36 11 41.1 7.8 28.7 Cohort 1 Maximum Minimum % Right- Censored Standard deviation Mean Lifetime (months)

Measuring Customer Lifetime for Non-Contractual Relationships (contd.)

Profit Calculation

Net-present value of profit is calculated on an individual customer basis for the period of 36 months as:

where LT  i = individual net-present lifetime profit for 36 months

GCti = gross contribution in month t for customer i ,

Cti = mailing cost in month t for customer i ,

0.0125 = monthly discount rate (based on 0.15 rate per year)

Test of the Propositions

Proposition 1:

Could customers with shorter tenure might actually be more profitable than long-term customers, a claim that runs counter to the theoretical expectations of a relationship perspective?

Which group of customers is of more interest to the firm, the one that buys heavily for a short period or the one with small spending but with long-term commitment?

Test of the Propositions (contd.)

Proposition 2

Examine the profitability evolution visually

Analyze the sign of the slope coefficient

The exact specification of the regression is:

Profits = a s + b 1s *Dummy + b 2s *t s + error

where t = month, b is = regression coefficient, s =segment,

Dummy = 1 if first purchase month, else 0

Proposition 3

Compute the ratio of promotional costs in a given period over the revenues in the same period

Proposition 4

Whether longer-life customers do pay higher prices as compared to shorter-life customers

Tests of Propositions - Results (Cohort 2 results in parentheses) High Lifetime Revenue Low Lifetime Revenue 63.54 (64.47) 0.065 (0.064) 11.67 (12.57) 257.96 (284.20) 783 (942) 47.97 (46.80) 0.141 (0.143) 2.41 (2.67) 50.49 (53.67) 1208 (1504) Average Item Price Mailing Cost/ Sales Ratio Relative Profit ($/month) Lifetime Profit per Customer ($) # of customers Av: Item Price Mailing Cost/ Sales Ratio Relative Profit ($/month) Lifetime Profit per Customer ($) # of customers Short Life time Segment 3 Segment 4 58.43** (58.25)** 0.063* (0.062)* 8.18 (9.31) 289.83 (322.03) 1322 (1546) 47.74 (48.72) 0.128 (0.124) 1.43 (1.56) 50.85 (55.26) 889 (973) 5 ) Average Item Price 4) Mailing Cost/ Sales Ratio 3) Relative Profit ($/month) 2) Lifetime Profit per Customer ($) 1) # of customers 5) Av: Item Price 4) Mailing Cost/ Sales Ratio 3) Relative Profit ($/month) 2) Lifetime Profit per Customer ($) 1) # of customers Long Life Time Segment 1 Segment 2

Interpretation of Results

Difference between Segment 1 and Segment 3 is not significant

** Difference between Segment 1 and Segment 3 is significant at  = 0.05

Both long-term customers (Segment 1) and short-term customers

(Segment 3) constitute the core of the firm’s business

Relationship between lifetime and profits can be far from being positive and monotonic

In terms of profit per month, customers in Segment 3 are the most attractive of all

Segment 3 customers purchase with high-intensity, thus generating higher profits in a relatively shorter period of time

Interpretation of Results (contd.)

The mean relative profit for each segment is significantly different from the other segment at least at  = 0.05 (using the multiple comparison test)

Segment 1 customers are the most desirable set for the firm –

represents the loyalty effect at its best

For Segment 3 customers (high revenue but short lifetime), there appears to be a good match between offerings and desires but their relationship duration may be complicated by moderating factors

Dissatisfaction might occur for Segment 4 whose customers spend the lowest amount

Aggregate Profits ($) for Short-life Segments

Aggregate Profits ($) for Long-life Segments

Regression Analysis of Profits as a Function of Time

Dummy Coefficient Coefficient

Segment Intercept (a) for t =1 (b1) for t (b2) R2

1 12.11 (12.73) 45.77 (46.38) -0.13 (-0.14) .85 (.85)

2 n.s. (n.s.) 30.24 (30.91) 0.07 (0.071) .92 (.91)

3 19.40 (20.9) 57.85 (58.29) -0.70 (-0.75) .95 (.94)

4 3.25 (3.69) 29.53 (31.45) -0.14 (-0.15) .94 (.95)

Regression Results for t = 1 to 36 Months (Cohort 1) Validation Results in Parentheses (Cohort 2)

With the exception of Segment 2, the coefficient for the linear effect has a negative sign – highlights the negative profit trend over time for the 3 segments

All the coefficients for time are significant at  =0.01

Are the Costs of Serving Long-Life Customers Lower?

The ratio of mailing cost per dollar sales in the longer-life segment (Segment 1) is statistically not different from the mailing cost per dollar sales in the shorter-life segment (Segment 3)

In terms of cost efficiency, Segments 1 and 3 are the most attractive to the firm, although they have very different lifetime properties

The ratio of mailing cost and revenues – which is one measure of efficiency – need not necessarily be lower for long-life-customers

Do Long-Life Customers Pay Higher Prices?

The average price per item for segment 3 is significantly (  = 0.05) different from (and greater than) that of segment 1

The highest average price paid for a single product item is in Segment 3, the short-life segment

The highly profitable short-term customers seem to be less

sensitive to the product’s price

The higher spending (average prices paid) by Segment 3 customers may be due to some other benefit sought by them

Summary of Findings

A strong linear positive association between lifetime and profits does not necessarily exist

A static and a dynamic lifetime-profit analysis can exhibit a much differentiated picture: profitability can occur for the firm from high and low lifetime customers

Profits do not increase with increasing customer tenure: the cost of serving long-life customers is not lower

Long-life customers do not pay higher prices

Study 2: A model for Incorporating Customers’ Projected Profitability into Lifetime Duration Computation

Background and objectives

Empirically measure lifetime duration for non-contractual customer-firm relationships, incorporating projected profits

Understand the structure of profitable relationships and test the factors that impact a customer’s profitable lifetime duration

Develop managerial implications for building and managing profitable relationship exchanges

Conceptual Model of Profitable Customer Lifetime Earlier Study B-to-C context only Present Study B-to-C and B-to-B contexts Profitable Lifetime Duration Exchange characteristics Observed heterogeneity Customer Profitability Lifetime Duration Non-contractual setting Revenues Cost

Determine the contribution margin expected from each customer

in future periods based on the average of the contribution margins in the past

Determine for each future period, the probability that the customer will be alive and will transact with the firm

Combine these two components

Discount the expected contribution margin in each future period to its

Net Present Value (NPV) using the cost of capital applicable to the firm

If in a given month, cost of additional marketing efforts is greater than NPV, determine that the Profitable Lifetime Duration of the customer has ended

Estimating Profitable Lifetime Duration

Antecedents of Profitable Lifetime Duration

Predictor variables to incorporate into the model:

Exchange variables: e.g. Amount Purchased, Degree of Cross-buying, Degree of Focused-buying, Inter-purchase Time, Number of Product Returns, Ownership of Loyalty Instruments, and Mailing efforts undertaken by the firm

Customer Heterogeneity variables: e.g. Location and Income of the customer

Conceptually,

Profitable Lifetime = f (Exchange characteristics, Customer heterogeneity)

Duration

Research Methodology

The customer-firm interaction of Cohort 1 households is tracked for a 36-month time period,

Cohort 2 for 35 and Cohort 3 for a 34-month time period

The households are sampled randomly from all households that started in January, February, and

March 1995 respectively

The number of purchases ranges from 1 to 46 across the sample with a median number of 5

purchases, the median interpurchase time is 117 days, and the median transaction amount is $91

for each purchase

Cohort 1: 4202 observations Cohort 3: 2825 observations Cohort 2: 4965 observations Jan ‘95 Feb ‘95 Mar ‘95 Dec ‘97 Start Finish Database Structure for B-to-C Setting

Determining Profitable Customer Lifetime Duration

Calculation of net present value (NPV) of expected contribution margin (ECM it ):

NPV of ECM it = where ECM it = estimated expected contribution margin for a given month t , AMCM it = average contribution margin in month t based on all prior purchases since birth (updated dynamically), r = discount rate (15% on a yearly basis) i = the customer t = month for which NPV is estimated n = number of months beyond t , P( Alive) in = probability that customer i is alive in month n .

Determining Profitable Customer Lifetime Duration (contd.)

Decision of relationship termination

Formally, if NPV of Expected CM it < Cost of Mailing, the firm would decide to

terminate the relationship

Decision rule incorporates the cost of mailings and an average flat contribution

margin before mailings of 25 percent

Discount rate is assumed to be 15% per year

Calculation of finite lifetime estimate

Based on decision of relationship termination, average lifetime across Cohort 1 is 29.3 months, Cohort 2 is 28.6 months, and Cohort 3 is 27.8 months

Variability in lifetime duration evidenced through

a wide range between lowest and highest lifetime estimate

the standard deviation of the lifetime estimate

the relatively small value of s in the NBD/Pareto model

Analysis

In the proportional hazard model, the hazard rate hi(t) for individual i is assumed to take the form:

where

h 0 (t) is the baseline hazard rate

(x it  ) is the impact of the independent variables

h i (t) = h 0 (t) e x it 

Variables for Profitable Lifetime Model (-)Inverse U-shaped relationship for AIT and AIT 2 (Number of Days) 2 (Average Interpurchase Time it ) 2 (+) Inverse U-shaped relationship for AIT and AIT 2 Number of Days Average Interpurchase Time it Non-directional hypothesis Dummy: 1 = buys consistently in single dept. only 0 = all other Focus of Buying i (+) Number of departments shopped in Cross Buying it + Monthly spending level ($), moving average over 6 month period Purchase amount it ** Hypothesized Directional Impact on Profitable Lifetime Measured as Independent Variables Months Profitable Lifetime i * Measured as Dependent Variable

Variables for Profitable Lifetime Model (contd.) No directional hypothesis Age of individual in years Age i (+) Scale from 1 to 9 where 1 is < $10,000 and 9 is > 150,000 Income i (-) Number of people in 2 digit zip code Population Density No directional hypothesis 1 = more than 50 % of purchases in softgoods, 0 = more than 50 % of purchases in hardgoods Product Category i (+) Number of mailings sent in last 6 months (= 1 season) since current t , exponential decay, one month lag Mailings it (+) Ownership of Charge card. Dummy variable, 1 = owns card, 0 = no card Loyalty Instrument i (-) Proportion of returns (of sales) Returns it

Analysis (contd.)

The hazard of a lifetime event of a household i at time t is given as:

h i (t) = h 0 (t) EXP (β 1 Purchase Amount it + β 2 Cross Buying it + β 3 Focus of Buying i + β 4 Average Interpurchase Time it + β 5 (Average Interpurchase Time it ) 2 + γ 1 Returns it + γ 2 Loyalty Instrument i + γ 3 Mailings it + γ 4 Product Category i + δ 1 Population Density i + δ 2 Income i + δ 3 Age i )

Summary of Results Supported However, the relationship is negative, indicating that buying in only a single department results in shorter lifetime duration Supported However, the relationship is negative, indicating that buying in only a single department results in shorter lifetime duration Related to the Focused Buying behavior exhibited by customers 2 b Partial Support Only the linear term is significant Supported Related to Average Interpurchase Time in an inverse U-shaped manner whereby intermediate AIT is associated with the longest profitable lifetime 3 Not Supported However, the interaction of Returns with Purchase amount variable is significant Not Supported However, the interaction of Returns with Purchase amount variable is significant Inversely related to the proportion of merchandise returned by the customers. 4 Supported Supported Positively related to degree of cross-buying behavior exhibited by customers 2 a Supported Supported Positively related to the customer’s spending level 1 B-to-B Setting Result B-to-C Setting Result Description Profitable Customer Lifetime Duration is: Hypothesis

Summary of Results (contd.) Supported Supported Profitable Customer Lifetime Duration is positively related to the Income of the customer (B-to-C) or Income of the firm (B-to-B) 8 Not supported Supported Profitable Customer Lifetime Duration is higher for customers living in areas with lower population density (B-to-C) or businesses existing in lower population density (B-to-B) 7 Supported Supported Positively related to the number of mailing efforts of the company (B-to-C) or the number of contacts (B-to-B) 6 Supported Supported Positively related to the customer’s ownership of the company’s loyalty instrument (B-to-C) or the availability of line of credit (B-to-B) 5

Estimation of P (Alive)

Method-of-moment approach

Estimate the four parameters of the NBD/Pareto model ( r,  , s,  ) with a Fortran routine with likelihood:

where M is a random sample of customers and customer i made X i = x i purchases in (0 ,T i ) with the last transaction time at t i

The larger the value of the shape parameter r the more homogeneous the population of customers in terms of purchase rate

The larger the value of the shape parameter s the more homogeneous the population of customers in terms of dropout rate

The concentration in dropout rates,  , depends on the parameter s only

Estimation of P (Alive) (contd.)

Probability that a customer with a particular observed transaction history is still alive at time T since trial:

P [Alive | r,  , s,  , x, t, T] =

where a 1 = r+x+s, b 1 = s+1, c 1 = r+x+s+1, z 1 (y) = (  -  ) / (  +y),

F(a 1 , b 1 ; c 1 ; z 1 ) is the Gauss hyper geometric function,

r,  , s,  = model parameters,

x = number of purchases,

t = time since trial at which the most recent transaction occurred,

T = time since trial

Study 3 – A Model for Identifying the True Value of a Lost Customer

Conceptual Background

The value of a lost customer depends upon whether:

the customer defects to a competing firm or

disadopts the product category

Defection: The firm loses direct sales that customer would have brought in

Disadoption: Customer stops purchasing from that product category altogether

Affects the long term profitability by :

The loss of direct sales

Indirect effects of word of mouth, imitation, and other social effects

Modeling the Effects of Disadoption on the Value of a Lost Customer

Value of an average lost customer (VLC) is calculated as:

VLC =  VLC disadopter + (1-  ) VLC defectors

where  is the proportion of disadopters in a firm’s lost customers

Profit impact of a lost customer = sales estimate from new product growth model without disadoption – the sales estimate when the customer disadopts after certain time

Modeling the Effects of Disadoption on the Value of a Lost Customer (contd.)

Key determinants of the value of a lost customer:

The time when customer disadopts has the largest impact on the value of the lost customer; earlier disadoption causes more loss of money

The external influence, p has a negative impact

The internal influence, q has a positive impact on penetration because higher q signifies stronger word of mouth

Discount rate has positive impact on the value of lost customer

Summary

A study of the Life-time-Profitability relationship in a non-contractual setting highlights concern with the widespread assumption of a clear-cut positive lifetime-profitability relationship and underlines the importance of a differentiated analysis

The empirical evidence showed that (1) a strong linear positive association between lifetime and profits does not necessarily exist; (2) profits do not necessarily increase with increasing customer tenure, (3) the cost of serving long-life customers is not lower, and (4) long-life customers do not pay higher prices